Advertisement

Spin–orbit hybrid entangled channel for spin state quantum teleportation using genetic algorithms

  • Francisco Domínguez-SernaEmail author
  • Fernando Rojas
Article
First Online:
  • 103 Downloads

Abstract

We present a physical model of spin quantum teleportation protocol (QTP) in a triple quantum dot array using a genetic algorithm approach. The information to teleport is spin-coded in one electron confined in a single quantum dot (SQD). The remaining double quantum dot (DQD) system has just an electron with spin that includes spin–orbit interaction. Charge and spin of the electron get hybridized with the site occupancy having two intrinsic quantum degrees of freedom. The DQD is prepared in a hybrid spin–orbit entangled (HES) Bell-like state with tunneling and site energies as time-dependent control parameters that are optimized by means of genetic algorithms (GAs). The hybrid entangled resources that we obtained allow spin-charge quantum state teleportation with a fidelity of 0.9972 and are used as a resource channel to establish the QT protocol. The spin state of the electron in the SQD interacts with the DQD spin–orbit entangled channel via a modulated exchange interaction to emulate Alice’s joint measurement required for QT with GA parameter control. A charge detection measurement in one of the DQD systems is sufficient to have the spin state teleported up to a unitary transformation. A specific joint measurement and unitary transformation were selected to test the protocol, and we obtain fidelity of 0.99 for the QTP. The quantum circuit models for both the spin–orbit entangled state and the teleportation are determined from the analysis of the stages of the controlled quantum dynamics obtained from the GA approach.

Keywords

Quantum teleportation Hybrid entangled states Genetic algorithms Quantum control Coupled quantum dots Spin–orbit interaction 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The first author expresses his gratitude to CONACyT-México for the scholarship received and upholds that most part of this work was developed as part of his master thesis.

References

  1. 1.
    Jozsa, R., Linden, N.: On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. A Math. Phys. Eng. Sci. 459(2036), 2011–2032 (2003).  https://doi.org/10.1098/rspa.2002.1097 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009).  https://doi.org/10.1103/RevModPhys.81.865 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pirandola, S., Eisert, J., Weedbrook, C., Furusawa, A., Braunstein, S.L.: Advances in quantum teleportation. Nat. Photon. 9, 641–652 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881–2884 (1992)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Bennett, C.H., Brassard, G., Crépeau, C.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1898 (1993)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bouwmeester, D., Pan, J.W., Mattle, K., Eibi, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)ADSCrossRefGoogle Scholar
  7. 7.
    Riebe, M., Häffner, H., Ross, C.F., Hänsel, W., Benhelm, J., Lancaster, G.P.T., Wörber, T.W., Becher, C., Schmidt-Kaler, F., James, D.F.V., Blatt, R.: Deterministic quantum teleportation with atoms. Nature 429(17), 734–737 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Contreras-Pulido, L.D., Aguado, R.: Entanglement between charge qubits induced by common dissipative environment. Phys. Rev. B 77(15), 155,420 (2004)CrossRefGoogle Scholar
  9. 9.
    Bernien, H., Hensen, B., Pfaff, W., Koolstra, G., Blok, M.S., Robledo, L., Taminiau, T.H., Markham, M., Twitchen, D.J., Childress, L., Hanson, R.: Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86 (2016).  https://doi.org/10.1038/nature12016 ADSCrossRefGoogle Scholar
  10. 10.
    Morton, J.J., Lovett, B.W.: Hybrid solid-state qubits: the powerful role of electron spins. Annu. Rev. Condens. Matter Phys. 2(1), 189–212 (2011).  https://doi.org/10.1146/annurev-conmatphys-062910-140514 ADSCrossRefGoogle Scholar
  11. 11.
    Gao, W.B., Fallahi, P., Togan, E., Delteil, A., Chin, Y.S., Miguel-Sanchez, J., Imamog̃lu, A.: Quantum teleportation from a propagating photon to a solid-state spin qubit. Nat. Commun. 4, 2744 (2013).  https://doi.org/10.1038/ncomms3744 ADSCrossRefGoogle Scholar
  12. 12.
    Dresselhaus, G.: Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100(2), 580–586 (1955)ADSCrossRefGoogle Scholar
  13. 13.
    Perel, V.I., Tarasenko, S.A., YAssievich, I.N., Ganichev, S.A., Bel’kov, V.V., Prettl, W.: Spin-dependent tunneling through a symmetric semiconductor barrier. Phys. Rev. B 67, 201,304 (2003)CrossRefGoogle Scholar
  14. 14.
    Bang, J., Yoo, S.: A genetic-algorithm-based method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem. J. Korean Phys. Soc. 62(12), 2001 (2014).  https://doi.org/10.1038/nature12016 CrossRefGoogle Scholar
  15. 15.
    Holland, J.C.: Adaptation in Natural and Artificial Systems, primera edn. The University of Michigan Press, Michigan (1975)Google Scholar
  16. 16.
    Krause, J., Reitze, D., Sanders, G., Kuznetsov, A., Stanton, C.: Quantum control in quantum wells. Phys. Rev. B 57(15), 9024–9034 (1998)ADSCrossRefGoogle Scholar
  17. 17.
    Navarro-Muñoz, J.C., Rosu, H.C., López-Sandoval, R.: Genetic algorithm optimization of entanglement. Phys. Rev. A 74, 52308 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    van der Wiel, W.G., De Franceschi, S., Elzerman, J.M., Fujisawa, T., Tarucha, S., Kouwenhoven, L.P.: Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    Liu, Y.S., Yang, X.F.: Enhancement of thermoelectric efficiency in a double-quantum-dot molecular junction. J. Appl. Phys. 108, 023710 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    Menichetti, G., Grosso, G., Paravicini, P.: Analytic treatment of the thermoelectric properties for two coupled quantum dots threaded by magnetic fields. J. Phys. Commun. 2(5), 55026 (2018)CrossRefGoogle Scholar
  21. 21.
    Petta, J.R., Johnson, A.C., Taylor, J.M., Laird, E.A.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Koppens, F.H.L., Buizert, C., Tielrooij, K.J., Vinik, I.T., Nowack, K.C., Meunier, T., Kouwenhoven, L.P., Vandersypen, L.M.K.: Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Shi, Z., Simmons, C.B., Prance, J.R., King Gamble, J., Seng Koh, T., Shim, Y.P., Hu, X., Savage, D.E., Lagally, M.G., Eriksson, M.A., Friesen, M., Coppersmith, S.N.: Fast hybrid silicon double-quantum-dot qubits. Phys. Rev. Lett. 108, 140503 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Nilsson, M., Chen, I.J., Lehmann, S., Maulerova, V., Dick, K.A., Thelander, C.: Parallel-coupled quantum dots in InAs nanowires. Nano Lett. 17(12), 7847–7852 (2017).  https://doi.org/10.1021/acs.nanolett.7b04090 ADSCrossRefGoogle Scholar
  25. 25.
    Hetano, T., Tokura, Y., Amaha, S., Kubo, T., Teraoka, S., Tarucha, S.: Excitation spectroscopy of few-electron states in artificial diatomic molecules. Phys. Rev. B 87, 241414 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    Sattler, K.D.: Handbook of Nanophysics. Nanoparticles and Quantum Dots, primera edn. University of Hawaii-Manoa, Honolulu (2010)Google Scholar
  27. 27.
    Gittings, J., Fisher, A.: Describing mixed spin-space entanglement of pure states of indistinguishable particles using an occupation-number basis. Phys. Rev. A 66(3), 032305 (2002).  https://doi.org/10.1103/PhysRevA.66.032305 ADSCrossRefGoogle Scholar
  28. 28.
    Wang, H., Kais, S.: Quantum teleportation in one-dimensional quantum dots system. Chem. Phys. Lett. 421(4–6), 338–342 (2006).  https://doi.org/10.1016/j.cplett.2006.01.093 ADSCrossRefGoogle Scholar
  29. 29.
    Visser, R.L., Blaauboer, M.: Deterministic teleportation of electrons in a quantum dot nanostructure. Phys. Rev. Lett. 96, 246801 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    Bader, S., Parkin, S.: Spintronics. Annu. Rev. Condens. Matter Phys. 1(1), 71–88 (2010).  https://doi.org/10.1146/annurev-conmatphys-070909-104123 ADSCrossRefGoogle Scholar
  31. 31.
    Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195–200 (1964)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Haupt, R.: Comparison between genetic and gradient-based optimization algorithms for solving electromagnetics problems. IEEE Trans. Magn. 31(3), 1932–1935 (1995).  https://doi.org/10.1109/20.376418 ADSCrossRefGoogle Scholar
  33. 33.
    Zingg, D.W., Nemec, M., Pulliam, T.H.: A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization. Revue européenne de mécanique numérique 17(1–2), 103–126 (2008).  https://doi.org/10.3166/remn.17.103-126 CrossRefzbMATHGoogle Scholar
  34. 34.
    Carbonneau, P.: Genetic algorithms in astronomy and astrophysics. Astrophys. J. Suppl. Ser. 101, 309–334 (1995)ADSCrossRefGoogle Scholar
  35. 35.
    Hill, S., Wootters, K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78(26), 5022–5025 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    Nielsen, M., Chuang, I.L.: Quantum Computation and Quantum Information, 1st edn. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  37. 37.
    Studer, M., Walser, M.P., Baer, S., Rusterholz, H., Schön, S., Schuh, D., Wagscheider, W., Enssin, K., Salis, G.: Role of linear en cubic terms for the drift-induced Dresselhaus spin-orbit splitting in a two-dimensional electron gas. Cond. Mat. Hall, pp. 1–7 (2010)Google Scholar
  38. 38.
    Bonestel, N.E.D., Stepanenko, D., DiVincenzo, D.P.: Anisotropic spin exchange in pulsed quantum gates. Phys. Rev. Lett. 87, 207901 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de OpticaCentro de Investigación Científica y de Educación Superior de EnsenadaEnsenadaMexico
  2. 2.Departamento de Física Teórica, Centro de Nanociencias y NanotecnologíaUniversidad Nacional Autónoma de MéxicoEnsenadaMexico

Personalised recommendations

Cite article

Buy options